Squares in the 40s

48 is 2 below 50, so $48^2$48² is ${\left(50-2\right)}^2$(50 − 2)²: 2500 − 200 − 200 + 4.

Two lots of 100 × 2 come off the 2500, which leaves 100 × 23.

Take the distance off 25, then attach its square: $48^2=2304$48² = 2304.